It was sixth consecutive defeat in the league for the Blues, their worst run since 1912, while the win moved Forest six points clear of the relegation zone with three games remaining.
What compounded matters for Chelsea was that the visitors made plenty of changes to their starting XI with one eye on the second-leg of the Europa League semi-final against Aston Villa on Thursday.
Forest took the lead after just two minutes when Nigeria international Taiwo Awoniyi found himself unmarked at the far-post and headed in a Dilane Bakwa cross.
The start went from bad to worse for the hosts when Malo Gusto fouled Awoniyi in the box and a penalty was awarded, following a VAR check, with Igor Jesus stepping up and making no mistake from the spot.
The home team thought they had found a way back into the contest in first-half stoppage-time when youngster Jesse Derry was upended in the box and a penalty given, but Cole Palmer saw his effort from 12 yards saved by Matz Sels.
The sound of the halftime whistle brought boos from the furious home crowd and the mood did not get better when Forest made it 3-0 soon after the interval.
Awoniyi completed his brace in the 52nd minute after the Nigeria forward tapped in a low square pass from Morgan Gibbs-White.
Chelsea grabbed a late consolation goal through Joao Pedro in found the back of the net, their first in six Premier League encounters.
Moises Caicedo has outlined his long-term vision at Chelsea after committing his future to the club until 2033, expressing confidence in both his own development and the squad's upward trajectory.
Tottenham gave their Premier League survival hopes a boost with an excellent performance and 2-0 victory against Aston Villa at Villa Park on Sunday.
Liverpool manager Arne Slot says he wants to finish in the highest position in the Premier League ahead of crucial tie against rivals Manchester United at Old Trafford on Sunday.
Arsenal manager Mikel Arteta heaped praise on his players performance in 3-0 victory over Fulham in the Premier League clash at Emirates Stadium on Saturday.
